Swap index

ABSTRACT

A set of indices is provided which allows accurate tracking of interest rate swap (IRS) markets. The indices are calculated using market data and synthetic purchasing and selling of synthetic interest rate swaps utilizing the present market data. The value of the synthetic interest rate swaps are the basis for the value of a particular index. The purchasing and selling of the synthetic interest rate swap occurs at a frequency to minimize effects of shortening terms on the index. One subset of the IRS indices reflects a plain-vanilla swap for a specific term of years. Another subset of the IRS indices reflects a spread between two specific terms of years. A third subset of the IRS indices reflect two spreads, sometimes referred to as a butterfly, between a middle term of years and a shorter term of years and the same middle term of years and a longer term of years.

This application is a continuation-in-part application claiming priorityto PCT International Patent Application No. PCT/US07/73775, filed Jul.18, 2007, which designates the United States of America and which claimsthe benefit of U.S. Provisional Patent Application Ser. No. 60/807,674,filed Jul. 18, 2006.

BACKGROUND OF INVENTION

A derivative is an investment, often in the form of a financialinstrument such as an agreement representing shares, from which payoffsover time are derived from the performance of assets (such ascommodities, shares or bonds), interest rates, exchange rates or indices(such as a stock market index, consumer price index (CPI) or an index ofweather conditions). The performance of the asset, interest rate,exchange rate or index can determine the amount or timing of thepayoffs, or both. All details regarding the amount and timing of thepayoff as well as the underlying assets, i.e. the value of the financialinstrument, are subject to an agreement defining these details. Portionsof the agreement apply to all financial instruments issued thereunderwhile portions of the agreement specific to the particular financialinstrument, i.e. number of shares and beginning value of the underlyingasset, are fully defined in the financial instrument. The main types ofderivatives are futures, forwards, options and swaps. A swap is where afirst party exchanges their future cash flow for the future cash flow ofa second party.

In the field of derivatives, a popular form of swap is the interest rateswap (“IRS”), in which one party exchanges a stream of interest foranother party's interest stream. IRSs are normally ‘fixed againstfloating’, i.e. the first party exchanges cash flow related to a loanmade at a fixed interest rate for cash flow to a second party related toa loan at a variable rate of interest. IRSs can also be ‘fixed againstfixed’ or ‘floating against floating’ rate swaps. The IRS agreement isentered into between two counterparties under which each agrees to makeperiodic payment to the other for an agreed period of time based upon anotional amount of principal. The principal amount is notional becausethere is no need to exchange actual amounts of principal in a singlecurrency transaction. A notional amount of principal is required inorder to compute the actual cash amounts that will be periodicallyexchanged.

IRSs are often used by companies to alter their exposure tointerest-rate fluctuations, by swapping fixed-rate obligations forfloating rate obligations, or swapping floating rate obligations forfixed-rate obligations. By swapping interest rates, a company is able tosynthetically alter their interest rate exposures and bring them in linewith management's appetite for interest rate risk.

Usually, one “leg” of an IRS involves quantities that are known inadvance, known as the “fixed leg”, the other leg involves quantitiesthat are not known in advance, known as the “floating leg”. The floatingleg, i.e. the floating interest rate obligation, must therefore be“reset” against an agreed reference rate, which will become known atsome point before payment or settlement takes place. For instance theparties might agree to pay 50 basis points (0.5%) over the LIBORmeasured on the 1st trading day of every 3rd month. The payment scheduleis often, but not always, timed to coincide with the resets. LondonInterbank Offered Rate (“LIBOR”) is a reference rate that varies dailybased on the interest rates at which banks offer to lend unsecured fundsto other banks in the London wholesale (or “interbank”) money market.Ideally, the determination of the reference rate must be outside thecontrol of the counterparties, otherwise a conflict of interest willarise. Typically, the reference rate is some figure made publiclyavailable by a third party information vendor, or by governmentagencies, e.g. LIBOR. Once a component of the floating leg is fixed (or“reset”), the fixed and floating components can be swapped or settled(typically one or two days after the fixing date).

Party F (for “fixed rate”) holds a fixed-rate loan, party V (for“variable rate”) holds a variable-rate loan. In a swap, F will make thepayments on V's loan and vice versa. There is no change in the balancesheets of either party, because the principal, i.e. the underlying‘notional’ amounts, offset one another and stay where they were. Inother words, what is called a $1 billion swap typically involves amountsmuch smaller than $1 billion. Thus, Party V agrees to pay Party Fperiodic interest rate payments of LIBOR+50 bps (bps=basis points=0.01%)in exchange Party F agrees to pay Party V periodic interest ratepayments fixed at 3.00%. Note that there is no exchange of the principalamounts and that the interest rates are on a “notional” (i.e. imaginary)principal amount. Also note that the interest payments are settled innet. Thus, if LIBOR is 1.20% when payments are due then LIBOR+50bps=1.70%; the fixed rate of 3.00% less this 1.70% means that Party Vreceives the ‘net’ of 1.30%. The fixed rate (3.00% in this example) isreferred to as the swap rate. If the underlying notional amount were $1billion and the revenue flow is calculated once annually, Party F wouldowe Party V $13,000,000. In the same example, if the net payment for theswap were calculated quarterly then Party F would owe Party V $3,250,000. This is because the interest rate is annualized and the termis one quarter of the year.

Trading an IRS is one of the more common forms of over-the-counterderivatives. It is the most widely used derivative in terms of itsoutstanding notional amount, but it is not standardized enough and doesnot have the properties to easily change hands in a way that will let itbe traded through a futures exchange like an option or a futurescontract. That is, even though the term ‘plain vanilla’ can be appliedto the swap, variables in any given swap are different enough thatstandardization is very difficult. Such variables include the notionalamount, the variable rate, the fixed rate, the swap/credit spread, theterm (in years), risk of nonpayment by any single participant, currencyetc. Thus, the liquidity of even the plainest of plain vanilla swaps islow.

The present value of a plain vanilla (i.e. straightforward) swap can becomputed using standard methods of determining the present value of thecomponents. Two things should be kept in mind when thinking about the‘value’ of a particular swap. First, when the swap is entered into thevalue of the swap to either party is typically zero. That is, the fixedand/or variable interest rate is ‘set’ (taking all publicly availableinformation into account), e.g. by varying the fixed rate or the bpsadded to LIBOR, such that the cash flow from F to V is equal to the cashflow from V to F for the entire term of the swap. A party is not goingto enter into a swap such that the future value of the swap starts outas a liability. One exception is where Party F pays Party V to enterinto a swap that is a liability, i.e. has a negative present value, toParty V. The payment from party F to party V is precisely the same asthe liability of the swap to Party V. Second, some variability is goingto be introduced over the life of the swap. Typically, this variabilitycomes in the form of one leg of the swap being subject to a variableinterest rate. Thus, the series of payments based on variable rates,from Party V, are determined at the agreed dates of each payment.

The most obvious difficulty to be overcome in attaching a present valueto a swap would seem to be the fact that the future stream of floatingrate payments is unknown. At the time the swap is entered into, only theactual payment rates of the fixed leg are known in the future. This isliterally true because it is not known with certainty what the 6 monthUS dollar LIBOR rate will be in 12 months time or 18 months time.However, markets possess a considerable body of information about therelationship between interest rates and future periods of time. Anestimation of the future rates affecting the floating leg can be derivedfrom the yield curve, to be further discussed below.

There is a large and liquid market in interest bearing securities issuedby governments. Liquid means that the price of a security is well knownto all market participants and, thus, it is typically very easy toconvert a “liquid” financial instrument into cash or vice versa bybuying or selling that instrument. These securities pay interest on aperiodic basis and are issued with a wide range of maturities. Principalon these government securities is repaid only at maturity and at anygiven point in time the market values these securities to yield whateverrate of interest is necessary to make the securities trade at their parvalue. It is possible, therefore, to plot a graph of the yields of suchsecurities vs. their varying maturities. This graph is known generallyas a yield curve, i.e. the relationship between future interest ratesand time.

The classic example of a yield curve is the US Treasury yield curve, anexample of which is shown in FIG. 1. Thus, yield curve 1 discloses that,at a particular point in time for which yield curve 1 is applicable, a 5year U.S. government bond had a yield of approximately 4% and a 20 yearbond had a yield of approximately 4.5%. For example, at a certain timeof a particular day in November, 2005, all of the available data puttogether revealed that the ‘market’ believed that the yield of a 5 yearU.S. bond was 4% and the yield of a 20 year U.S. bond was 4.5%. All ofthis data regarding the market was compiled in yield curve 1.

Another government security is the zero coupon bond. The zero couponbond does not pay interest at periodic intervals. Instead it is issuedat a discount from its par or face value but is redeemed at par, theaccumulated discount which is then repaid representing compounded or“rolled-up” interest. A graph of the internal rate of return (IRR) ofzero coupon bonds over a range of maturities is known as the zero couponyield curve 2 in FIG. 2. FIG. 2 also shows the par yield curve 3.

Finally, at any time the market is prepared to quote an investor forwardinterest rates. If an investor wishes to place a sum of money on depositfor six months and reinvest that money after maturity for a further sixmonths, then the market will quote today a rate at which the investorcan re-invest his deposit in six months time. The six month forwarddeposit rate is not a ‘guess’; it is a mathematically derived rate whichreflects an arbitrage relationship between current (or spot) interestrates and forward interest rates, i.e. the six month forward interestrate is the rate of interest which eliminates any arbitrage profit. Theforward interest rate will leave the investor indifferent as to whetherhe invests for six months and then re-invests for a further six monthsat the six month forward interest rate or whether he invests for atwelve month period at today's twelve month deposit rate. FIG. 3 showsan example of the forward curve 4. FIG. 3 also shows a zero coupon yieldcurve 5 and a par bond yield curve 6.

Thus, the market possesses sufficient information concerning the yieldgenerated by existing instruments over future periods of time. Themarket has the ability to calculate forward interest rates which willeliminate arbitrage profit with spot interest rates. All of thisinformation is available from publicly available sources. Futurefloating rates of interest can be calculated, therefore, using theforward yield curve. This, however, is not sufficient to calculate thefuture payments due under the swap and, thus, the mark to market valueof the swap at a given point in time.

As discussed above, the aggregate set of cashflows due under any swapis—at inception—zero. That is, the net present value of both the fixedrate stream of payments and the floating rate stream of payments in afixed to floating IRS is zero and the net present value of the completeswap must be zero. Since the floating rate payments due under the swapcan be calculated (as explained above) it follows that the fixed ratepayments will be such that when they are deducted from the floating ratepayments and the net cash flow for each period is discounted at theappropriate rate given by the zero coupon yield curve, the net presentvalue of the swap will be zero. It might also be noted that the actualfixed rate produced by the above calculation represents the par couponrate payable for that maturity if the stream of fixed rate payments dueunder the swap are viewed as being a hypothetical fixed rate security.

Each future variable rate payment is calculated using the forward rate,from the forward rate curve, for each respective payment date. A seriesof future cash flows is thus calculated. Each cash flow is discounted bythe zero coupon rate for the date of the payment, calculated from thezero coupon yield curve data. Zero coupon rates are used because theserates are for bonds which pay only one cash flow. The IRS is thereforetreated like a series of zero coupon bonds.

The fixed rate offered in the swap is the rate which values the fixedrate's payments at the same value as the variable rate payments usingtoday's forward rates. Therefore, at the time the contract is enteredinto, there is no advantage to either party, and therefore the swaprequires no upfront payment.

During the life of the swap the same valuation technique is used. Overtime, many of the factors described above, including the yield curve,the zero coupon bond curve and the forward curve will have changed. Infact, these curves change continuously. Based on these changes, mark tomarket accounting for the swap will almost always reveal the swap to bean asset to one party and a liability to the other.

Reversing or terminating an IRS is often necessary or desirable. Asdiscussed previously, the shape of the curves used to price the swapinitially will change over time. We begin with the assumption thatshortly after a swap there is an increase in forward interest rates,i.e. the forward yield curve steepens. Since the fixed rate payments dueunder the swap are fixed, this change in the prevailing interest rateenvironment will affect future payments made under the floating ratearm. This benefit will accrue to Party F and will represent a cost tothe Party V. If the future net cash flows of the swap are computed fromthe latest forward yield curve and discounted at the appropriate newzero coupon rate for each future period, i.e. reflecting the currentzero coupon yield curve, the positive net present value result reflectshow the value of the swap to Party F has risen. Correspondingly, itdemonstrates how the value of the swap to Party V has declined.

Using common financial terminology, this valuation of the swap may alsobe called “mark to market” of the IRS. If, having done this, thefloating rate payer wishes to terminate the swap with the fixed ratepayer's agreement, then the positive net present value (“mark tomarket”) figure we have calculated represents the termination paymentthat will have to be paid to the fixed rate payer. Alternatively, if thefloating rate payer wishes to cancel the swap by entering into a reverseswap with a new counterparty for the remaining term of the originalswap, the net present value figure represents the payment that thefloating rate payer will have to make to the new counterparty in orderfor him to enter into a swap which precisely mirrors the terms andconditions of the original swap.

Some basic reasons for swap transactions will now be discussed. Acompany with excellent credit will pay less to borrow money underidentical terms than a less creditworthy company. The extra paid by theless creditworthy company is referred to as a “credit quality spread”.This spread is typically greater in relation to fixed interest rateborrowings than it is for floating rate borrowings. This spread alsotypically increases with maturity. The swap party making fixed ratepayments (Party F) in a swap is predominantly the less creditworthyparticipant. Companies can lower their costs of borrowing by using swapsin conjunction with credit quality spreads. IRSs are used by a widerange of banks, non-financial operating companies, insurance companies,mortgage companies, investment vehicles and trusts, government agenciesand sovereign states for one or more of the following reasons: 1. Tolower funding costs; 2. To hedge interest rate exposure; 3. To implementasset or liability management strategies; 4. To create types ofinvestments not currently obtainable; 5. To obtain higher yields frominvestment assets; and 6. Speculation in relation to future movements ininterest rates.

The advantages of IRSs include the following: 1. A floating-to-fixedswap increases the certainty of an Party V's future obligations; 2.swapping from fixed-to-floating rate may save Party V money if interestrates increase (conversely, if interest rates decrease, Party F willhave the positive net cashflow); 3. swapping allows issuers to revisetheir debt profile to take advantage of current or expected futuremarket conditions; and 4. IRSs are a financial tool that potentially canhelp issuers lower the amount of debt service.

Investors, for their own reasons, enter into transactions to buy or sellan IRS of a particular duration while simultaneously selling or buyingan IRS of a longer duration. This activity, though of great value to theinvestor, is expensive as it includes IRS transaction brokerage fees andthe IRS bid offer spread for two periods. Should that investor then wishto exit the trade, the same bid offer has to be crossed and transactionfees again paid. This method of trading is antiquated by nature if onlyby the exposure to losses in attempting to trade large amounts of twoswap periods at the same time; as such, trades of this type lendthemselves perfectly to an index eliminating such risks.

There is also a lack of a viable bench mark for which corporate bondscan be pegged. Although treasuries can be used, the spread activity is amore accurate barometer of interest movement when it comes to corporatelending.

To trade traditional IRS there are various costs incurred, includingcrossing the bid offer spread, cost of credit, and transaction/brokeragefees. In addition, unlike most notes or bonds where the maturity isfixed, the IRS market completes each transaction out of spot (2 workingdays forward of the trade date) and with the end date being theduration, i.e. 2, 5, 10, 30 years, should the trader wish to reverse herposition at any time after the original trade date there is an obviousmismatch in the end date. This increases exposure and createscomplications in back office management of positions which, in turn,increases possible trading errors. Should a trader wish to takeadvantage of the yield curve by executing 2 years and executing 10years, in order to be properly duration weighted the trader has tocomplete a 2 year IRS having a notional amount of approximately $400million for a notional amount of $100 million in the 10 year IRS. Thiscreates liquidity risk because executing the required notional amount of2 years is multiplicatively more difficult than executing the requirednotional amount of ten years. Liquidity risk as for instance should shetrade the 10 year leg the subsequent volume required to complete the 2year leg of the trade may not be available, or the reverse should shetrade the 2 years once the volume is completed the 10 year price mayhave moved against the trader, both trading methods are cumbersome andcan create unwanted positions these can be the most expensive of allcosts associated with trading the IRS, as the traders options arelimited to running the unwanted position in the hope that the curvetrade can be completed or unwind the trade and cross the bid offer andabsorb any price changes to reverse it.

BRIEF DESCRIPTION OF THE FIGURES

FIG. 1 is a graph showing an example of a bond yield curve;

FIG. 2 is a graph showing examples of a zero coupon bond curve and a paryield curve; and

FIG. 3 is a graph showing examples of a forward curve, a zero couponyield curve and a par bond yield curve.

SUMMARY OF THE INVENTION

Indices are described herein to accurately reflect IRS of varyingduration. Investors wishing to protect themselves from adverse movementsin an interest rate curve, i.e. by way of the yield curve steepening orflattening, may buy or sell based on the appropriate index. What isbought or sold is, at its most basic, an agreement where the variableterm to the agreement is the index. The greater the change in the valueof the index from the time the agreement begins, the more the agreementis worth to one of the two parties to the agreement. The difference inthe underlying index from inception of the agreement to the terminationof the agreement is multiplied by some value set at the beginning of theagreement to determine how much one party to the agreement owes theother party to the agreement, i.e. a notional amount. Just like an IRS,this agreement is a derivative. That is, the agreement is a financialinstrument that has its value derived from an underlying asset. As inany derivative, market participants enter into an agreement to exchangemoney, assets or some other value at some future date based on theunderlying asset. In this case, the underlying assets are syntheticinterest rate swaps that are calculated to accurately reflect or trackan actual IRS of agreed to parameters.

The index products described herein are for the periods that arecurrently quoted over the on-the-run US treasuries which are 2 year, 3year, 5 year treasuries, the 10 year note and the 30 year bond. Theseare quoted as semi bond points and as spread to treasury 2×3, 2×5, 2×10,2×30, 3×5, 3×10, 3×30, 5×10, 5×30, 10×30. Also to be included arebutterfly trades which involve buying or selling the wings and sellingor buying the body. These include 2×3×5, 2×5×10, 2×10×30, 3×5×10,3×10×30 and 5×10×30.

It is also believed that new market participants will be attracted tocurve trading as credit issues and back office restrictions bar themfrom trading at present.

IRS spreads are set each day for option settlement. It would be alreadyaccepted duration weighting standards which would apply and be reset atthe end of each calendar month.

A preferred embodiment of the present invention is derivative financialinstrument comprising a nominal amount; a financial instrument valuedirectly proportional to the nominal amount and directly proportional toa numerical index. The numerical index is proportional to an interestrate swap value determined from an interest rate swap. A first side ofthe interest rate swap has a first set of parameters for calculating afirst set of payments; and a second side of the interest rate swap has asecond set of parameters for calculating a second set of payments. Thesecond set of parameters includes a variable parameter not contained inthe first set of parameters. The value of the interest rate swap is thevalue of the first set of payments less the value of the second set ofpayments. In a preferred embodiment of the invention, the variableparameter is a variable rate of interest. In another preferredembodiment of the invention, the first set of parameters includes aninterest rate having a fixed rate over a term of the interest rate swap;and the second set of parameters includes an interest rate having avariable rate of interest over the term of the interest rate swap. In afurther preferred embodiment of the invention, the interest rate swap isa synthetic transaction. In a further preferred embodiment of theinvention, the financial instrument is easily purchased and sold on anessentially transparent market. In a further preferred embodiment of theinvention, a single counterparty exists to all purchases and sales ofthe derivative financial instrument. In a further preferred embodimentof the invention, the derivative financial instrument is either a boughtfinancial instrument or a sold financial instrument and further whereinthe financial instrument value for a bought financial instrumentincreases proportionally to the value of the interest rate swap and thefinancial instrument value for a sold financial instrument decreasesproportionally to the value of the interest rate swap. In a furtherpreferred embodiment of the invention, the interest rate swap is for anumber of years, the number of years being one of the first set ofparameters and the second set of parameters. In a further preferredembodiment of the invention, the variable parameter is a yield curvefrom a debt obligation having a term equal to the number of years of theinterest rate swap. In a further preferred embodiment of the invention,the first set of payments are discounted by a zero coupon bond yieldcurve. In a further preferred embodiment of the invention, the value ofthe variable parameter is determined from publicly available informationnot under the control of the buyer or seller of the financialinstrument. In a further preferred embodiment of the invention, thevalue of the variable parameter changes constantly during at least aportion of a business day and the numerical index is calculated inreal-time along with the variable parameter change. In a furtherpreferred embodiment of the invention, the interest rate swap is for aset number of years, and further wherein: neither the first set ofparameters or the second set of parameters includes shortening of theterm defined by the set number of years as a parameter in calculatingthe first set of payments or the second set of payments. All of thepreferred embodiments for the derivative financial instrument involvinga first swap are applicable for the derivative financial instrumentcomprising a first swap and a second swap.

A preferred embodiment of the present invention is derivative financialinstrument comprising a nominal amount; a financial instrument valuedirectly proportional to the nominal amount and directly proportional toa numerical index. The numerical index is proportional to an interestrate swap value determined from an interest rate swap. A first side ofthe interest rate swap has a first set of parameters for calculating afirst set of payments; and a second side of the interest rate swap has asecond set of parameters for calculating a second set of payments. Thesecond set of parameters includes a variable parameter not contained inthe first set of parameters. The value of the interest rate swap is thevalue of the first set of payments less the value of the second set ofpayments. In a preferred embodiment of the invention, the variableparameter is a variable rate of interest. In another preferredembodiment of the invention, the first set of parameters includes aninterest rate having a fixed rate over a term of the interest rate swap;and the second set of parameters includes an interest rate having avariable rate of interest over the term of the interest rate swap. In afurther preferred embodiment of the invention, the interest rate swap isa synthetic transaction. In a further preferred embodiment of theinvention, the financial instrument is easily purchased and sold on anessentially transparent market. In a further preferred embodiment of theinvention, a single counterparty exists to all purchases and sales ofthe derivative financial instrument. In a further preferred embodimentof the invention, the derivative financial instrument is either a boughtfinancial instrument or a sold financial instrument and further whereinthe financial instrument value for a bought financial instrumentincreases proportionally to the value of the interest rate swap and thefinancial instrument value for a sold financial instrument decreasesproportionally to the value of the interest rate swap. In a furtherpreferred embodiment of the invention, the interest rate swap is for anumber of years, the number of years being one of the first set ofparameters and the second set of parameters. In a further preferredembodiment of the invention, the variable parameter is a yield curvefrom a debt obligation having a term equal to the number of years of theinterest rate swap. In a further preferred embodiment of the invention,the first set of payments are discounted by a zero coupon bond yieldcurve. In a further preferred embodiment of the invention, the value ofthe variable parameter is determined from publicly available informationnot under the control of the buyer or seller of the financialinstrument. In a further preferred embodiment of the invention, thevalue of the variable parameter changes constantly during at least aportion of a business day and the numerical index is calculated inreal-time along with the variable parameter change. In a furtherpreferred embodiment of the invention, the interest rate swap is for aset number of years, and further wherein: neither the first set ofparameters or the second set of parameters includes shortening of theterm defined by the set number of years as a parameter in calculatingthe first set of payments or the second set of payments.

Another preferred embodiment of the present invention has a first andsecond interest rate swap used for determining a spread interest rateswap value which, in turn, is used for determining a spread IRS index.The first interest rate swap is essentially unchanged. A first side ofthe second interest rate swap has a third set of parameters forcalculating a third set of payments and a second side of the secondinterest rate swap has a fourth set of parameters for calculating afourth set of payments, the fourth set of parameters including a secondvariable parameter not contained in the third set of parameters. Thespread interest rate swap value is the value of the first set ofpayments less the value of the second set of payments plus the value ofthe fourth set of payments less the value of the third set of payments.All of the preferred embodiments for the derivative financial instrumentinvolving a first swap are applicable for the derivative financialinstrument comprising a first swap and a second swap.

Another preferred embodiment of the present invention has a first,second and third interest rate swap used for determining a butterflyinterest rate swap value which, in turn, is used for determining abutterfly IRS index. The first and second interest rate swap areessentially unchanged. A first side of the third interest rate swap hasa fifth set of parameters for calculating a fifth set of payments and asecond side of the third interest rate swap has a sixth set ofparameters for calculating a sixth set of payments, the sixth set ofparameters including a third variable parameter not contained in thefifth set of parameters. The butterfly interest rate swap value is thevalue of the first set of payments less the value of the second set ofpayments plus the value of the fourth set of payments less the value ofthe third set of payments plus the value of the fifth set of paymentsless the value of the sixth set of payments.

Another preferred embodiment of the present invention is a derivativefinancial instrument comprising a value determined from a nominal amountand an index; the index calculated from an underlying interest rate swapwhich is synthetically sold and immediately rebought at a predeterminedfrequency.

DETAILED DESCRIPTION OF THE INVENTION

A market index keyed to the IRS market described above provides enormousbenefits to current IRS market participants as well as new IRS marketparticipants. The index would not usually involve any underlying“notional amounts” for the loans. Rather, the basic value of the indexto the purchaser or seller of a financial instrument based on the indexwould be valued completely by the amount of money invested. Someexamples contained herein use United States Dollars (“USD”) and fixedincome products most familiar to investors and investment servicesprofessionals operating in the United States. Other possible indicesencompassed by the herein described invention should in no way beassumed to be limited to United States dollars or the exemplary fixedincome products presented. In fact, these indices are applicable to anymarket, currency, mixed currencies and analogous fixed income productswherein the tools, e.g. yield and zero coupon curves, herein describedare either available or translatable.

A market has developed, as traders wish to capture the difference inyield between two medium term IRS periods, known as an over the countermedium term IRS forward spread semi-bond market. The following indicesseek to provide a market to satisfy this demand, giving the investor theability to achieve full replication of one or more IRSs, whilst loweringtransaction costs, offering completeness, investability, accurate data,complete data and clear published open rules. These goals, besides beingdesirable in their own right, will result in high liquidity of thefinancial instruments sold and traded in light of these indices.

Setting up IRS indices, i.e. fixing of proper index calculation rules,is the first step in starting and maintaining, in good and reliablemanner, a market for products valued by said index, i.e. derivativeproducts. The indices include three types of indices to start and tomaintain afterwards: 1. Indices for IRS Trades: For every governmentsecurity lifetime from 2 to 30 (full) years=29 Indices. Index reflectscost to buy the trade, i.e. to enter a swap as fixed-rate receiver andfloating-rate payer, but it is also possible to sell the index and thusenter the trade as the floating-rate receiver. 2. Indices for IRS SpreadTrades: For two different security lifetimes. Purchasing such an indexresults in effectively buying the longer maturity security and sellingthe short maturity security. Selling such an index results ineffectively selling the long maturity and buying the short maturity. Allpossible combinations of benchmark government security lifetimes (2, 3,5, 10, 30)=10 indices: 2×3, 2×5, 2×10, 2×30, 3×5, 3×10, 3×30, 5×10,5×30, and 10×30. 3. Indices for IRS Butterfly Trades: For certaincombinations of three benchmark government security lifetimes buy thebody (middle maturity) and sell the wings (shorter and longermaturities). Selling the index results in selling the body and buyingthe wings. The most prevalent butterfly trades=6 indices: 2×3×5, 2×5×10,2×10×30, 3×5×10, 3×10×30, 5×10×30; though any other combinations arepossible. The indices of all three groups together are 29+10+6=45indices.

The purpose of each index is to reflect the movements in the IRS marketby entering synthetic IRS, IRS spread and IRS butterfly trades on theorigin day. The “origin day” is the starting date of a given index. Thevalue of an index is computed on an ongoing real-time basis for all ofthe synthetic positions entered. This computation incorporates everychange of every parameter upon which the synthetic IRS is based, e.g. onevery day which is a business day either in NY or in London or both, inreal-time.

Some aspects on the main structure of the USD IRS market: The USD IRSmarket is defined in relation to the standard on-the-run US Treasurybonds. These benchmark bonds have lifetimes of (at issue) 2, 3, 5, 10and 30 years. IRS rates are defined for the benchmark lifetimes of 2, 3,5, 10 and 30 years: 1. Take the mid yield of the given on-the-run USTreasury bonds; 2. Add a spread in basis points, one spread for bidlevel and one spread for offer level, to that mid yield; and 3. Resultis the IRS rate, one rate for bid level and one rate for offer level.

When considering the swap lifetime, the quotes for the swaps always arefor full years, traded spot (today+2 trade days), regardless of thedaily shortening of lifetime of the US Treasury bonds to which thespreads refer to. This leads to the situation that, when a new USTreasury bond is issued, which from then on is the new on-the-runtreasury bond of the respective benchmark lifetime 2, 3, 5, 10 or 30,the spreads have to be adjusted by IRS traders (sources for the rates),to the effect that the resulting IRS rates remain the same as(immediately) before the new issue was out.

The spreads, and thus the resulting IRS rates, for the lifetimes of 11and 12 years, are taken directly from the 10 year Treasury bond. Thespreads, and thus the resulting IRS rates, for all other lifetimes (4,6, 7, 8, 9, 13 . . . 29) are generated on base of an interpolationbetween the lifetimes of the nearest two benchmark treasury bonds, e.g.the spread for 4 years is quoted using the mid yield of the 3 yearTreasury and the mid yield of the 5 year Treasury, divided by 2.Numerous sources of IRS rates, e.g. banks, are available for setting abenchmark. Deviations between different providers usually are small andnumerous providers can be averaged.

There are two types of IRS day count conventions: a) “Semi Bond”: fixedrate paid 30/360 semi-annually modified following (UK business days) andfloating rate 3-month LIBOR actual/360 quarterly modified following (UKbusiness days); and b) “Annual Money”: fixed rate paid actual/360annually modified following (UK business days) and floating rate 3-monthLIBOR actual/360 quarterly modified following (UK business days). Thestandard IRS type is Semi Bond (above a).

Dates and Times: All indices shall base on swaps that follow the SemiBond rule. All indices shall be calculated using mid swap rates, theoffer and bid differences shall not be taken into account. Start of thedaily valuations shall be 09:00 CET=08:00 UK. There shall be a dailyfixing of the index values for index history building purposes, at 10:00NY=16:00 CET=15:00 UK. The end of the daily valuations shall be 17:00NY=23:00 CET=22:00 UK.

Regarding notional amounts, all indices shall start with a particularindex value of, e.g., 100.00. Thus, there is no need to use a notionalamount. Every index value can be converted into a USD nominal amount bymultiplication. For the calculation of the indices reflecting SpreadTrades and Butterfly Trades however, there need to be done certainnotional amount adjustments. For spread trades, the notional amount ofthe long leg (which is bought into the index) can be set to $25 millionand the notional amount of the short leg (which is sold into the index)shall be adjusted so that the modified duration of the short leg, at thestart of the index, or at rebalancing time respectively, shall be thesame as the modified duration of the long leg. For butterfly trades, thenotional amount of the body (which is bought into the index) may be setto $25 million. The body may then be considered as divided into twoparts of $12.5 million each. The notional amounts of each of the wings(which are sold into the index) shall be adjusted so that its modifiedduration, at the start of the index, or at rebalancing timerespectively, shall be the same as the modified duration of the halfbody.

Index data to publish regarding the 45 indices (29+10+6=45) can becreated and tracked for IRS trades, IRS spread trades and IRS butterflytrades. Each of these indices stands alone and has no affect on theother indices; all indices are handled separately based on external,publicly available information. The index values will reflect the valueof the IRS, IRS spread and IRS butterfly trades. On the initial day,their value is assigned an index value of 100.00. The index figures canbe considered synthetic.

As long as index values, daily change values and interpolated swap ratesfor non-benchmark year's lifetime would be sufficient as output values,US Treasury bond data or issuance is not needed. Should however spreadto treasuries values be desired as part of the indices service, it couldbe used. The index would need to hold and maintain data regarding theon-the-run benchmark US Treasury bonds, including the processes of rollfrom old to new on-the-run benchmark Treasuries, which involvesmonitoring Treasury issuance very closely, and acting on changes in anarrow timeframe on every Treasury issue day. One would need to takecare of the Treasury's prices and yields, and reverse engineer thespread to Treasuries from the swap rates used for index calculations,and the yields of the respective Treasury benchmark bonds. The onlyexcess value would be the calculation of spread to Treasury Mid values,where obviously spread to Treasury offer and bid values are alreadythere.

To avoid synthetic cash flow paid out from the synthetic swap positions,all IRS trades may be sold and newly bought synthetically. Thisrebalancing should occur as frequently as necessary to increase theaccuracy of the index. Frequencies of annually, semi-annually,quarterly, monthly, daily, every trading day and numerous times per dayare all possible. Monthly rebalancing, used in the example herein, isutilized in a preferred embodiment of the present invention. Presumingappropriate automation is present, daily rebalancing is a most preferredembodiment of the present invention. Rebalancing also avoids theshortening of lifetimes of all positions which at beginning are fullyears, so that no position lifetime can be less than the respectivenumber of years less the rebalancing frequency. The effect of increasedrebalancing frequency is a reduction of the effect of shortening oflifetimes of the synthetic positions. It is expected that forrebalancing frequency of one day or greater, i.e. hourly or everysecond, the effect of shortening lifetimes may be negligible.

To avoid deferrals resulting from holidays or weekends, monthlyrebalancing shall always be done on the same day every month, e.g., thesecond Wednesday of every month. The rebalancing procedures, whichinclude the recalculation of notional amounts for spread and butterflytrades indices, shall take place on this day at a specified andconsistent time. For example, 10:00 NY=16:00 CET (Central EuropeanTime)=15:00 UK. If the rebalancing frequency is daily, a most preferredembodiment would rebalance at a time when all information is availableand not changing, e.g. after-hours for all relevant markets.

In order to calculate a particular IRS index, all of the synthetic IRSpositions which have been reset at the last rebalancing event (e.g., the2^(nd) Wednesday of every month or daily) have to be valuated. Therebalancing event results in the rates and maturities of the syntheticIRS matching the values of the current (e.g., 2^(nd) Wednesday 15:00 UKor daily) curves, as opposed to the curves underlying the synthetic IRSfrom the previous rebalancing date. This rebalancing is exactly the sameas the process of valuing the swap at inception; all of the same datasources are used for an IRS set to begin that day. Thus, whether atrebalance or inception, the index is reset such that the value of theswap to either side is zero. Rebalancing, because it is a syntheticprocess, is accomplished such that it has no effect on the index. Afterrebalancing, as the underlying rates which determine swap rates changeaccording to the market movements, and the remaining lifetimes of theIRS positions decrease day by day during the month (e.g., from secondWednesday to second Wednesday); the IRS positions, and thus the index,change in value. In the event that rebalancing is done daily or everybusiness day, the effect of lifetime of the IRS position should beminimal.

For the valuation of IRS positions, a zero interest rate curve iscreated from the current LIBOR rates and the current swap rates, takinginto account the day count conventions of the market, e.g., actual/360quarterly for the LIBOR variable leg and 30/360 semi-annually for thefixed/swap leg, both modified following. The discount factors from thiscurve are multiplied by the cash flows of the synthetic IRS positions tovaluate, and the results are added up to result in the values of thesynthetic IRS positions.

The value of any of the 2 to 30 years synthetic IRS positions isreflected in the change to the respective 2-30 years IRS index, comparedto the respective 2 to 30 years IRS index value reached at the lastrebalancing time. For any of the 2 to 30 years IRS positions, therespective change amount is added to the index value of the lastrebalancing time. The result is the current index value. Thus, thecurrent index value may be calculated by determining the change in valuesince the last rebalance and adding this change to the index determinedat the last rebalance. Alternatively, presuming the accuracy of thereal-time data that has caused the index in question to change with eachchange in the underlying curves that determine the value of thesynthetic IRS, the index may also be calculated “tick-by-tick” ofchanges in the underlying curves. Calculated from rebalance to rebalanceor “tick-by-tick”, the index value should be identical under eitherprocess.

For spread and butterfly interest rate positions, there is not only oneswap to valuate, but a portfolio of two (in case of spread positions) orthree (butterfly positions) IRS valuations to determine in rebalancing.For any of the spread and butterfly IRS positions, the value of itsrespective portfolio expresses the change to the respective index,compared to the index value reached at the last rebalancing time. Forany of the spread and butterfly IRS positions, the respective changeamount is added to the index value of the last rebalancing time. Theresult is the current index value. In the same manner as describedabove, the index may be calculated in real-time, “tick-by-tick”, toarrive at the same index value as calculated at rebalance.

For swaps paying semi-annually on the fixed leg and quarterly on thefloating leg (as in the USD market) at a horizon of 30 years, for eachtime the index is calculated there are 60 payment dates starting fromsettlement. These payment dates are designated t_(i), starting from t₀(settlement) and running up to t₆₀ (which occurs 30 years from t₀). Foreach t_(i) we have a current swap rate s_(i). For valuation we need tocalculate the present value, d_(i), factor for each t_(i). Let c_(ij) bethe amount due under a swap running i periods at date t_(j). Normallythis is s_(i)/2, but may differ slightly because of the modifiedfollowing usance. Example: Let's have settlement (t₀) be 8 Aug. 2007,and let's assume the 4 year swap rate is 5%. The coupon payment days(t₁; t₂; t₃; t₄; t₅; t₆; t₇; t₈) for this swap are (Aug. 10, 2007; Feb.11, 2008; Aug. 11, 2008; Feb. 10, 2009; Aug. 10, 2009; Feb. 10, 2010;Aug. 10, 2010; Feb. 10, 2011; Aug. 10, 2011) (adjusted for weekends) andthe swap fix payments (c₈₁; C₈₂; C₈₃; C₈₄; C₈₅; C₈₆; C₈₇; c₈₈) are(2.513888889; 2.5; 2.486111111; 2.5; 2.5; 2.5; 2.5; 2.5), according tothe modified following usage. As a swap paying the current swap rate haszero value, we have:

${{\sum\limits_{j = 1}^{i}{d_{j}c_{ij}}} + {100d_{i}}} = 100$

Rearranged this gives:

${{\sum\limits_{j = 1}^{i}{d_{j}c_{ij}}} + {100d_{i}}} = {{{\sum\limits_{j = 1}^{i - 1}{d_{j}c_{ij}}} + {d_{i}c_{ii}} + {100d_{i}}} = {{{\sum\limits_{j = 1}^{i - 1}{d_{j}c_{ij}}} + {d_{i}\left( {c_{ii} + 100} \right)}} = 100}}$$\mspace{20mu} {d_{i} = {\left( {100 - {\sum\limits_{j = 1}^{i - 1}{d_{j}c_{ij}}}} \right)/\left( {100 + c_{ii}} \right)}}$

This is used to calculate the d_(i) iteratively.

If swap rates are not quoted semi-annually, missing rates areinterpolated linearly from the quoted rates. Further, there are no swaprates for 1 year and 6 months. Therefore the LIBOR rates for 6 and 12months are used for the calculation of the present value factors forthese payments.

To calculate the index, the swaps set at the latest rebalancing areused. These are the swaps we have to valuate to calculate the index. Thesame notation as above is used, but with upper case letters. If thelatest rebalancing has been done on the recent 2^(nd) Wednesday of themonth, to calculate the index for the Friday following this day(provided there are no holidays between) use: T_(i)=the settlement datei periods from that Friday; S_(i)=the swap rate fixed at the latestrebalancing for the swap running i periods; C_(ij)=the amount payed bythe swap running i periods at date T_(j); and D_(i)=The present valuefactor for a specific settlement date T_(i). Also needed: L=The nextpayment on the floating leg (calculated from the 3 month LIBOR ratefixed for the floating leg); T_(L)=the date of the next floating legpayment date; and D_(L)=The present value factor for T_(L). T_(i),S_(i), C_(ij) and L are known from the fixing. D_(i) is needed for thevaluation. If it is not the rebalancing day, the t_(i) differ from theT_(i) and the D_(i) have to be interpolated from the d_(i). This is doneusing exponential interpolation (i.e., linear interpolation on thelogarithms of the d_(i)). (Example: Assume that settlement is 10 Aug.2007 and we've calculated d₆ (10 Aug. 2010) and d₇ (10 Feb. 2011) as0.8638 and 0.8430. We need to interpolate D₇ for 6 Jan. 2011. Calculate:Time to 10 Aug. 2010 is 3 years, time to 10 Feb. 2011 is 3+184/365years=3.5041 years, time to 6 Jan. 2011 is 3+149/365 years=3.4082 years.Therefore,D₇=exp(ln(0.8638)+(ln(0.8638)−(ln(0.8430))/(3.5041-3)*(3.4082-3)))=0.8469.)For D_(L) (nearly 3), D₀ (nearly 6) and D₁ (nearly 12 months) the LIBORrates are taken into account for interpolation. (e.g. D_(L): discountfactors for two and three months are calculated directly from the twoand three month LIBOR rate, then interpolation is performed as describedabove).

Having the D_(i) calculated, the swaps may be valued. Let P_(i) denotethe current present value of the swap running i periods at the latestrebalancing.

Thus:

$P_{i} = {{\sum\limits_{j = 1}^{i}{D_{i}C_{ij}}} + {100D_{i}} - 100 - \left( {{D_{L}L} - {100\left( {1 - D_{L}} \right)}} \right)}$

Note that at the rebalancing, where T_(i)=t_(i), S_(i)=s_(i) andD_(i)=d_(i), all P_(i) are 0. Let the current Swap Index value (for iperiods) be noted by x_(i), and the Swap Index value at the latestrebalancing by X_(i). Then:

x _(i) =X _(i) +P _(i)

This gives the current value of the index.

DETAILED EXAMPLE

This example shows the calculation of the index. A 3 year index and itsmovement from 11th to 12th of July 2007 is shown. July 11th is a 2ndWednesday in a month where the index is rebalanced. Tables 1 and 2 showthe LIBOR and swap rates fixed on that day and shows the calculation ofthe factors used to value a swap, designated P_(v). The swap rates areused as the coupons for the next months.

TABLE 1 Trade: Jul. 11, 2007 Settlement: Jul. 13, 2007 LIBOR Months Rate(act/360) 2 5.34% 3 5.36% 6 5.38% 12 5.39563% Swap Rate (30/360 Yearssemiannually) 2 5.35% 3 5.393%

TABLE 2 Time 30/360 Time Day mod. follow. Coupon P_(V) factor 3 mos 15Oct. 2007 0.5 14 Jan. 2008 0.502777778 0.973096583 1 14 Jul. 2008 0.55.413055% 0.947862402 1.5 13 Jan. 2009 0.497222222 5.381527% 0.9234560912 13 Jul. 2009 0.5 5.350000% 0.899833961 2.5 13 Jan. 2010 0.5 5.371500%0.875906759 3 13 Jul. 2010 0.5 5.393000% 0.852424438

Table 1 shows the LIBOR and swap rates fixed on 11th July (forsettlement on July 13th). Table 2 shows the calculations. The secondcolumn of Table 2 shows the payment dates (dd/mm/yy) of the swapstarting at July 11th with settlement July 13th. Note that, due toweekends, they are not always on the 13th. The third column of Table 2shows the times to be used as the length of the coupon period ending atthat day (calculated 30/360 modified following as the fixed leg on theswap pays). This means that the payment of the swap's fixed leg on a dayin the second column is its swap rate multiplied by the correspondingnumber in the third column. Calculating for the P_(v) factors, thevalues for 0.5 and 1 year can be calculated from the LIBOR rates. Forthe others, the swap rates for 1.5, 2, 2.5 and 3 years are needed to usethe usual bootstrap algorithm (with a semiannually grid). The rates for2 and 3 years are quoted and shown under COUPON. For 2.5 yearsinterpolation from the quoted 2 and 3 years is used. Similarly, 1.5years is interpolated from the quoted 1 and 2 years. Here, at firstglance, seems to be a problem as there is no swap rate for a 1 yearswap. However, the correct rate for a hypothetical 1 year swap can beeasily calculated from the P_(v) factor for 0.5 and 1 year. This is usedfor interpolation for 1.5 years. Having set up the rates in COUPONcolumn, the P_(v) factors can be easily calculated.

Applying these P_(v) factors calculated from the swap rates at fixing onthe swaps set up here at rebalancing (e.g. the 3 year swap paying 5.393%fix and 5.36% floating), we would get a zero value. However, as the swaprates will change after fixing on the same day, the P_(v) factors willchange, giving the swap a non-zero value and thus driving the index on areal time basis.

Things get more complicated on the next day where the maturity of theswap set up at rebalancing (which represents the index) has shortened.Tables 3, 4 and 5 show the LIBOR and swap rates fixed on that day.Again, the tables shows the calculation of the P_(v) factors for a swapstarting on that day. This time, however, the P_(v) factors are neededfor payment dates of the swap set up on the previous day (therebalancing day) too. Tables 3, 4 and 5 shows how these areinterpolated.

TABLE 3 Trade: Jul. 12, 2007 Settlement: Jul. 16, 2007 LIBOR Months Rate(act/360) 2 5.34% 3 5.36% 6 5.386% 12 5.41625% Swap Rate (30/360 Yearssemiannually) 2 5.398% 3 5.445%

TABLE 4 Time 30/360 PV Time Time Day mod. follow. Coupon factor (actual)2 months 17 Sep. 2007 0.99074152 0.172131 3 months 16 Oct. 20070.98648732 0.251366 0.5 16 Jan. 2008 0.5 0.97320907 0.502732 1 16 Jul.2008 0.5 5.433712% 0.94780872 1.000000 1.5 16 Jan. 2009 0.5 5.415856%0.92298642 1.502732 2 16 Jul. 2009 0.5 5.398000% 0.89897694 2.000000 2.519 Jan. 2010 0.50833333 5.421500% 0.87443824 2.510929 3 16 Jul. 20100.49166667 5.445000% 0.85110874 3.000000

TABLE 5 Day Time (actual) PV factor −0.00930161 15 Oct. 2007 0.248633880.98663371 −0.01360481 −0.01345642 14 Jan. 2008 0.49726776 0.97349582−0.02715635 −0.02686175 14 Jul. 2008 0.99453552 0.94808421 −0.05360257−0.05331196 13 Jan. 2009 1.49453552 0.92338587 −0.08014076 −0.0797080713 Jul. 2009 1.99180328 0.89936759 −0.1064979 −0.10606344 13 Jan. 20102.49453552 0.87521508 −0.13417361 −0.13328562 13 Jul. 2010 2.991803280.85149456 −0.16121538 −0.16076217

Table 3 shows the LIBOR and swap rates fixed on 12th July (forsettlement on July 16th). The algorithm used regarding Tables 1 and 2 isused to get the P_(v) factors for the payment dates of a swap startingon (settlement) July 16th. This is shown in Table 4.

However, to get the value of the swap set up the day before, we needP_(v) factors for the payment dates of a swap starting on July 13^(th),i.e. settlement. These are interpolated in Table 5. The method used isexponential interpolation, which means a linear interpolation on thelogarithms of the P_(v) factors. That is, take the logarithms of theP_(v) factors, interpolate linearly on them, then take the exponentialof the interpolated value to get the desired P_(v) factor. This methodis also known as the method of constant forward rates. Therefore, forboth day columns of Table 4 and Table 5, the time in years fromsettlement (16/07/07) is calculated. Note that (as opposed to thepayment calculation under the TIME 30/360 Column, where 30/360calculation is used) we count the actual days here to get a smoothdiscount function. The actual interpolation values are given in the lastthree columns of Table 5.

The valuation of the swap using the discount factors calculated in theP_(v) factor Column of Table 5 can be found in Table 6, which shows thevaluation of the swap on that day, using the P_(v) factors from Tables3-5.

TABLE 6 Day Payment P_(V) factor Fixed Leg 14 Jan. 2008 2.711481%0.973495817 14 Jul. 2008 2.696500% 0.948084206 13 Jan. 2009 2.681519%0.923385867 13 Jul. 2009 2.696500% 0.899367592 13 Jan. 2010 2.696500%0.875215078 13 Jul. 2010 2.696500% 0.851494558 99.902874% Value of FixedLeg Floating Leg 15 Oct. 2007 1.399556% 0.986633708 1.354737%100.044220% Value of Floating Leg Swap Value −0.141345% Value ofReceiver Swap Index Value at 11 Jul. 2007: 98.785758% Index Value at 12Jul. 2007: 98.644413%

Table 6 is the valuation of the 3 year swap set up at July 11th(settlement July 13th) on the next day (July 12th, settlement July16th). For ease of calculation, the principal at each leg of the swap isincluded. So we regard the fixed leg as a bond, the floating leg as afloater. The Value of the Fixed Leg is straightforward. For the floatingleg: A floater set up on July 16^(th) (settlement) but paying on 13th(i.e. a floater with a short first coupon) would have par value whenpaying the ‘correct’ first coupon (i.e. the coupon interpolated from theLIBOR rates). So we can measure the difference from par by measuring the(present value of) the difference between the ‘correct’ first coupon tothe current first coupon fixed on the previous day. The correct firstcoupon can be calculated from the interpolated P_(v) factor and is1.354737%. The current coupon is 1.399556%. The value of the floater inthis example is thus 100.044220%. So the swap's value to the receiver isfixed leg—floating leg, which gives −0.1413. This means that the indexfor 3 years has gone down by this amount on July 12th compared to July11th. Adding this to the value of July 11th (which is known by this timeas 98.785758) gives the index value for July 12^(th), i.e. and 98.644413.

The values of both legs are calculated and combined and give the changeof the present value of the swap compared to 11.07.07. This change isadded to the index value of 11.07.07 to give the index value for12.07.07. Although the example uses a short maturity swap of 3 years,the calculation method is the same for longer maturities.

When the index is rebalanced once a month on the second Wednesday itmeans that for succeeding days (July 13th, July 16th etc.) the swapstarted on July 11th is valued, so we get its change compared to July11th (where its value was zero) and add it to the index value on July11th to get the index value of the day. This continues until the indexis rebalanced next time (on August 8th).

If the rebalancing is done daily instead of once a month, in accordancewith a preferred embodiment of this invention, this would not change thebasic methodology, the difference would just be to value a swap set upthe previous day and add this to previous day's index value. This, asopposed to valuing a swap set up on the last second Wednesday and addthis to the last second Wednesday's index value.

Real Time Market Data and Swap Parameters

Real-time market data providing environments would be the mostappropriate input data sources in handling the IRS indices contemplatedherein. Assuming that spread to Treasury values can be omitted asproject output values (see above), all calculations can be performedusing: Quoted IRS Semi Bond Swap rates; and standard USD LIBOR rateswhich are necessary as sources for interpolations (LIBOR for 1, 2, 3, 6months and 1 year).

The source for IRS Semi Bond Swap rates should be fixed. Again, manysources for IRS Semi Bond Swap rates exist. The standardization andpossible averaging from multiple sources would need to be built in anddisclosed as part of the index. Transparency and resultant liquidity arekey to the indices. There are quotes available for both offer and bid,for 2-15 years in steps of 1 year, then for 20, 25 and 30 years. The midswap rates for all of these lifetimes need to be calculated, and thenthe interpolations of mid swap rates for the lifetimes of 16-19, 21-24and 26-29 years, using the 15, 20, 25 and 30 year rates respectively,would have to be done. These rates would be the source for thevaluations for all synthetic swaps, and thus for the calculation of allindices.

On days where there is a business day in NY but not in UK, the LIBORrates of the previous UK business day should be used unchanged.

One solution is that the index valuations could be performed usingfinancial market software which can valuate IRS positions. The projectsoftware has a real-time interface which would use IRS semi bond quotesand LIBOR rates, and the real-time distribution of the index values too.The solution would need to be capable of holding synthetic IRSportfolios and calculating the standard output values described above.

The trade contents include: Trade date: The date on which thetransaction occurs. Notional principal amount: The specific dollaramount on which the exchange of interest payments are based. Value date:The date on which the agreement takes effect. Maturity date: Theduration of the IRS modified following. Spread to Treasury: Thedifference between the current US Treasury yield and the rate that bankscharge each other for lines of credit. The price discrepancy is anindicator of credit risk. Treasury hedge: A treasury transaction made inorder to reduce the risk of adverse price movements. Treasury hedge #1and #2: When there is no current on-the-run Treasury for the IRS period,the treasury hedge is calculated using a combination of the adjacentcurrent on-the-run treasury before and after the maturity date. Treasuryprice: Treasury price expressed as a percentage of par. Treasury price#1: Treasury price expressed as a percentage of par. Treasury price #2:Treasury price expressed as a percentage of par. Treasury yield: Thecoupon rate divided by the market price. Treasury yield #1: When thereis no current on-the-run treasury for the period requiring the IRS, aninterpolated yield is calculated using the adjacent current on-the-runtreasury before and after the maturity date. Treasury yield #2: Whenthere is no current on-the-run treasury for the period requiring theIRS, an interpolated yield is calculated using the adjacent currenton-the-run treasury before and after the maturity date. Fixed rate: therate that does not change for the duration of the IRS. Fixed rateinterest rate calculation: The day count convention that specifies howto count the number of days between two dates, and how to calculate thelength of an interest period when the period is smaller than a regularinterest period. Fixed rate payable: The date on which the fixed rate isscheduled to become payable. Fixed rate payments dates: The actual dateon which the fixed interest rate is paid. Floating rate: The interestrate that changes on a preset periodic basis for the duration of theIRS. First floating rate: The rate that applies to the first floatingperiod. First floating rate set for period ending: The date for whichthe first floating rate is to be applied. Floating rate interest ratecalculation: The day count convention that specifies how to count thenumber of days between two dates, and how to calculate the size of aninterest period when the period is smaller than a regular interestperiod. Floating rate reset dates: The dates on which the floating rateis adjusted and reset. Floating rate payable: The dates on which thefloating rate is scheduled to become payable. Floating rate paymentdates: The date on which the floating interest rate is paid. Interestheld and compounded: Interest which is calculated on the notionalprincipal amount plus the accumulated interest of prior periods. Paymentexchange: Payments of interest obligations based on the notionalprinciple amount. Mutual put: A zero premium put option exchanged byboth counterparties giving the right but not the obligation to excisethe option at market at a predetermined date.

Rates fixed at index inception: At mid market 2-year, 3-year, 5-year,10-year, and 30-year, current treasury yield.

Rates interpolated at mid market: 4-year, 6-year, 7-year, 8-year,9-year, 13-year, 14-year, 15-year, 16-year, 17-year, 18-year, 19-year,20-year, 21-year, 22-year, 23-year, 24-year, 25-year, 26-year, 27-year,28-year and 29-year, current treasury yield. 11-year and 12-year tradeuse at mid market 10-year current treasury yield. At mid market spreadto current treasury yield on the spot 2-year, 3-year, 4-year, 5-year,6-year, 7-year, 8-year, 9-year, 10-year, 11-year, 12-year,13-year,14-year, 15-year, 16-year, 17-year,18-year, 19-year, 20-year, 21-year,22-year, 23-year, 24-year, 25-year, 26-year, 27-year, 28-year, 29-year,30-year and spot 40-year.

3 month LIBOR may be used at index inception.

Rebalance dates: The date the United States Treasury new issue of the2-year note, 3-year note, 5-year note, 10-year note, or 30-year bondtrades current. The reopen of a current note or bond is not considered arebalance event or date. Treasury bills and tips are excluded.Alternatively, the rebalance dates can be monthly on a particular day ofthe month, e.g. the second Wednesday of the month, or for shorterperiods such as daily or multiple times per day.

Rebalance time: If monthly, this needs to be set. For example, 10:00 amEastern United States.

Rates reset on rebalance dates: At mid market 2-year, 3-year, 5-year,10-year, and 30-year current treasury yield. Interpolated at mid market4-year, 6-year, 7-year, 8-year, 9-year, 13-year, 14-year, 15-year,16-year, 17-year, 18-year, 19-year, 20-year, 21-year, 22-year, 23-year,24-year, 25-year, 26-year, 27-year, 28-year, and 29-year currenttreasury yield. 11-year and 12-year trade use at mid market 10-yearcurrent treasury yield. IRS at mid market spread to current treasuryyield on the spot 2-year, 3-year, 4-year, 5-year, 6-year, 7-year,8-year, 9-year, 10-year, 11-year, 12-year, 13-year, 14-year, 15-year,16-year, 17-year, 18-year, 19-year, 20-year, 21-year, 22-year, 23-year,24-year, 25-year, 26-year, 27-year, 28-year, 29-year, 30-year and spot40-year.

Spread to Treasury Reference Source: At inception: Current mid market,vendor spread to current treasury prices or market poll. At rebalance:Take the IRS index mid price, take out the mid old treasury yield,resulting in a synthetic mid spread to treasury plus or minus thetreasury roll from the mid of the old issue to the mid of the new issue,reset at market mid spread to treasury 2-years thru 40-years.

End of day: For example, 5:00 pm Eastern United States.

IRS index Semi Bond Spread Trades can be for periods: 1a) 2-year×3-year;1b) 2-year×5-year; 1c) 2-year×10-year; 1d) 2-year×30-year; 2a)3-year×5-year; 2b) 3-year×10-year; 2c) 3-year×30-year; 3a)5-year×10-year; 3b) 5-year×30-year; 4a) 10-year×30-year. The IRS spreadrequires two simultaneous trades, buying or selling the shorter period(short leg) whilst the reverse (selling or buying) the longer period(long leg). Purchasing the index reflects to buy the longer period.Note: “IRS spread” not to be confused with a spread to treasury or bidoffer spread.

Short leg settings at origin: Trade date: Index origin date. Notionalprincipal amount: Duration weight. Value date: 2 good business days(spot). Maturity date: The duration of the IRS. Treasury hedge: Currenton-the-run. Treasury hedge amount: Determined at Rebalance. Fixed rate:At mid market current treasury yield, plus at mid market spread totreasury yield, semi bond. Spread to treasury: At mid market. Currenttreasury yield: At mid market. Current treasury price: At mid market.Fixed rate interest rate calculation: 30/360 adjusted bond basis. Fixedrate payable: Semi annual. Fixed rate payments dates: Semi annual.Floating rate: 3 month LIBOR. First floating rate: LIBOR. First floatingrate set for period ending: 3 month LIBOR. Floating rate interest ratecalculation: Actual/360. Floating rate reset: Quarterly. Floating ratepayable: Quarterly. Floating rate payment dates: Quarterly. Floatingrate held and compounded: No. Payment exchange: Net payment. Mutual put:No.

Reset at rebalance: Trade date: The day of the rebalance date. Notionalprincipal amount: Duration weight. Value date: 2 good business days(spot). Maturity date: The duration of the IRS. Spread to treasury: Atrebalance fixing. Treasury hedge: Current on-the-run. Treasury hedgeamount: Determined at origin or rebalance. Treasury price: At midmarket. Fixed rate: At mid current treasury yield, plus at spread totreasury yield fixing, semi bond. Fixed rate payments dates: Semiannual. Floating rate: 3 month LIBOR. First floating rate set for periodending: 3 month LIBOR. Floating rate payment dates: Quarterly.

Terms and conditions: Non business day: Modified following ISDAdocumentation, herein incorporated by reference. “ISDA” is theInternational Swaps and Derivatives Association which periodicallypublishes standards type publications used by the industry. Ref sourcefor floating rate: Telerate page 3750, herein incorporated by reference.Ref source Spread to treasury: IRS Index. Ref source for treasury yield:Publicly available.

Conditions: ISDA documentation, herein incorporated by reference.

Long leg settings at origin: Trade date: Index origin date. Notionalprincipal amount: 25 Million US Dollars. Value date: 2 good businessdays (spot). Maturity date: The duration of the IRS. Treasury hedge:Current on-the-run. Treasury hedge amount: Determined at origin orrebalance. Fixed rate: At mid market current treasury yield plus, at midmarket spread to treasury yield, semi bond. Spread to treasury: At midmarket. Treasury yield: At mid market. Treasury price: At mid market.Fixed rate interest rate calculation: 30/360 adjusted bond basis. Fixedrate payable: Semi annual. Fixed rate payments dates: Semi annual.

Floating rate: 3 month LIBOR. First floating rate: LIBOR. First floatingrate set for period ending: 3 month LIBOR. Floating rate interest ratecalculation: Actual/360. Floating rate reset: Quarterly. Floating ratepayable: Quarterly. Floating rate payment dates: Quarterly. Floatingrate held and compounded: No. Payment exchange: Net payment. Mutual put:No.

Reset at rebalance: Trade date: The day of the rebalance date. Valuedate: 2 good business days (spot). Maturity date: The duration of theIRS. Spread to treasury: At rebalance fixing. Treasury hedge: Currenton-the-run. Treasury hedge amount: Determined at origin or rebalance.Treasury price: At mid market. Fixed rate: At mid current treasuryyield, plus at spread to treasury yield fixing, semi bond. Fixed ratepayments dates: Semi annual. Floating rate: 3 month LIBOR. Firstfloating rate set for period ending: 3 month LIBOR. Floating ratepayment dates: Quarterly.

Terms and conditions: Non business day: Modified following ISDAdocumentation, herein incorporated by reference. Ref source for floatingrate: Telerate page 3750, herein incorporated by reference. Ref sourceSpread to treasury: IRS index. Ref source for Treasury yield: FTSE.

Conditions: ISDA documentation, herein incorporated by reference.

Note: It is standard market practice to apply the notional amount to themiddle leg or body, with the wings being duration weighted.

IRS index, IRS Semi Bond Trades Periods: 2-year, 3-year, 5-year,10-year, 11-year, 12-year, 30-year, 40-year. The index reflects to buythe swap.

Settings at origin: Trade date: Index origin date. Notional principalamount: 1 Million US Dollars. Value date: 2 good business days (spot).Maturity date: The duration of the IRS. Treasury hedge: Currenton-the-run. Treasury hedge amount: Determined at origin or rebalance.Fixed rate: At mid market current treasury yield, plus market spread totreasury yield mid, semi bond. Spread to treasury: At mid market.Treasury price: At mid market. Treasury yield: At mid market. Fixed rateinterest rate calculation: 30/360 adjusted bond basis. Fixed ratepayable: Semi annual. Fixed rate payments dates: Semi annual.

Floating rate: 3 month LIBOR. First floating rate: LIBOR. First floatingrate set for period ending: 3 month LIBOR. Floating rate interest ratecalculation: Actual/360. Floating rate reset: Quarterly. Floating ratepayable: Quarterly. Floating rate payment dates: Quarterly. Floatingrate held and compounded: No. Payment exchange: Net payment. Mutual put:No.

Resets at rebalance: Trade date: The day of the rebalance date. Valuedate: 2 good business days (spot). Maturity date: The duration of theIRS. Spread to treasury: At rebalance fixing. Treasury hedge: Currenton-the-run. Treasury yield: At mid market. Treasury price: At midmarket. Fixed rate: At mid current treasury yield mid, plus at spread toyield fixing, semi bond. Fixed rate payments dates: Semi annual.Floating rate: 3 month LIBOR. First floating rate set for period ending:3 month LIBOR. Fixed rate payments dates: Semi annual.

Terms and conditions: Non business day: ISDA documentation, hereinincorporated by reference. Ref source Spread to treasury: IRS Index. Refsource for treasury yield: FTSE. Ref source for floating rate: Teleratepage 3750, herein incorporated by reference.

Conditions: ISDA documentation, herein incorporated by reference.

Periods: 4-year, 6-year, 7-year, 8-year, 9-year, 13-year, 14-year,15-year, 16-year, 17-year, 18-year, 19-year, 20-year, 21-year, 22-year,23-year, 24-year, 25-year, 26-year, 27-year, 28-year, and 29-year. Theindex reflects to buy the swap.

Settings at origin: Trade date: Index origin date. Notional principalamount: 1 Million US Dollars. Value date: 2 good business days (spot).Maturity date: The duration of the IRS. Treasury hedge amount #1.:Determined at origin or rebalance. Treasury hedge amount #2.: Determinedat origin or rebalance. Fixed rate: At mid market interpolated currenttreasury yield, plus at market spread to treasury, semi bond. Treasuryprice #1: At mid market. Treasury price #2: At mid market. Treasuryyield #1: At mid market. Treasury yield #2: At mid market. Interpolatedtreasury yield: At market. Fixed rate interest rate calculation: 30/360adjusted bond basis. Fixed rate payable: Semi annual. Fixed ratepayments dates: Semi annual. Floating rate: 3 month LIBOR. Firstfloating rate: LIBOR. First floating rate set for period ending: 3 monthLIBOR. Floating rate interest rate calculation: Actual/360. Floatingrate reset: Quarterly. Floating rate payable: Quarterly. Floating ratepayment dates: Quarterly. Floating rate held and compounded: No. Paymentexchange: Net payment. Mutual put: No.

Resets at rebalance: Trade date: The day of the rebalance date. Valuedate: 2 good business days (spot). Maturity date: The duration of theIRS. Spread to treasury: At rebalance fixing. Treasury hedge #1.:Determined at origin or rebalance. Treasury hedge #2.: Determined atorigin or rebalance. Treasury price #1: At mid market. Treasury price#2: At mid market. Treasury yield #1: At mid market. Treasury yield #2:At mid market. Fixed rate: At mid current treasury yield fixing, plus atspread to yield fixing, semi bond. Fixed rate payments dates: Semiannual. Floating rate: 3 month LIBOR. First floating rate set for periodending: 3 month LIBOR. Fixed rate payments dates: Semi annual.

Terms and conditions: Non business day: ISDA documentation, hereinincorporated by reference. Ref source Spread to treasury: IRS index. Refsource for treasury yield: FTSE. Ref source for floating rate: Teleratepage 3750, herein incorporated by reference.

Conditions: ISDA documentation, herein incorporated by reference.

When there is no current treasury for the IRS period, an interpolatedyield is calculated using the closest current treasury before and afterthe maturity date.

The medium term IRS market realigns the spread to treasury instantly byadjusting the spread to treasury to accommodate for the roll between theold and new issues, this practice results in zero price discrepancy inthe medium term IRS semi bond market rates. When the market rolls fromthe old issue to the new, the IRS index rebalance emulates this marketpractice precisely, and will result in a zero price discrepancy in theIRS index. Hence forth it is entirely reasonable that the index itselfcan establish the rebalancing spread to treasury in establishing thecurrent spread to treasury by reverse calculating the IRS index priceand adjusting the resulting synthetic spread to treasury to accommodatefor the roll creating independence from third party vendors. Therebalance is in place in order maintain the rudiments of the indexperfectly inline with the spot IRS market. This will enable to set theindex at any time they see fit.

When there is no current treasury for the IRS period, the treasury hedgeamount is calculated using a combination of the closest currenton-the-run treasury before and after the maturity date.

These IRS indices have been described as accommodating the US Dollar IRSmarket for purposes of exemplary convenience. However, they can beapplied to any currency and even to multiple currencies in a singleindex. Adjustments in the IRS index can be made in order to reflect anycountries debt policies. Put another way, calculation of the IRS indexdisclosed herein is possible as long as the data regarding theunderlying curves is available for the asset in question.

On the index price page show the interpolated spread to treasury as theprice changes in the index this will not correlate with the index pricesbecause the treasury yield is always also changing. The index may bereverse priced to show treasury yield. It can be traded that way bytrading the index and USD swap spread only. A synthetically createdtreasury yield can also be created and, if this yield is different tothe current yield, the two products may be arbitraged. Also, the samecan be done with the spreads if the treasury yield is taken out and thespread differs; the spread in both can be traded to arbitrage them.

EXAMPLE OF SET OF GROUND RULES FOR MANAGING INDICES

Ground Rule 1:

1.1 The Index Series

1.1.1 The Index Series US Dollar Indices is a series of swaps indicescovering the principal interest rate swaps markets.

1.1.2 The series consists of four interest rate swaps indices: IndexSeries US Dollar Indices, Index Series Euro Indices, Index Series YenIndices, Index Series Sterling Indices.

1.2 These Ground Rules

1.2.1 These Ground Rules for the management of the Index Series USDollar Indices.

1.2.2 Further versions of these ground rules could define the specificdetails for the Euro, Yen, and Sterling Swaps Indices.

1.3 Index Series Objectives

1.3.1 The objective is to create and maintain a series of indices forthe international swaps markets for use as a benchmark and a tradingvehicle by the global investment community. To achieve this, we havesought to establish the Index Series as being: Comprehensive,Consistent, Flexible, Accurate, Investable, Transparent, Predictable,Representative, User-driven

1.4 Indices

1.4.1 All Index Series US Dollar Indices are calculated as real-timeindices and fixed at the end of the US business day however a fixingwill be taken at 14:00 GMT for history building purposes.

1.4.2 The Index Series US Dollar Indices has the following indices:Interest Rate Swaps—29 Indices: 2-30 year swaps; Swaps Spreads—10Indices: combinations of benchmark lifetimes (i.e. 2, 3, 5 10, 30); andButterfly Swaps—6 Indices: combinations of benchmark lifetimes (e.g.2×3×10).

1.5.1 Index Series US Dollar Indices consist of the main swap terms(i.e. 2-30 years) and Swap and Butterfly Indices for the benchmarklifetimes.

For better understanding of the index, some aspects on the mainunderlying structure of the USD swap market are: The USD IRS market isdefined in relation to the standard on-the-run US Treasury bonds. Thesebenchmark bonds have lifetimes of (at issue time) 2, 3, 5, 10 and 30years. IRS rates are defined as a result of spreads quoted versus USTreasury benchmark bond mid yields versus the benchmark lifetimes of 2,3, 5, 10 and 30 years, and using interpolations for the non-benchmarklifetimes. For Index Series US Dollar Indices, the “Semi Bond” standardUSD IRS day count convention is used: Fixed rate paid 30/360semi-annually modified following (UK business days) and floating rate3-month LIBOR act/360 quarterly modified following (UK business days)

1.6 Index Methodology

1.6.1 All indices are based on swaps that follow the standard IRS daycount convention in the respective market. All indices are calculatedusing mid swap rates, the bid and offer differences are not taken intoaccount. Start of the daily valuations are 09:00 CET=08:00 UK. There isa daily fixing of the index values for index history building purposes,at 10:00 NY=16:00 CET=15:00 UK. The end of the daily valuations is 17:00NY=23:00 CET=22:00 UK.

Notional amounts: Since all indices have started with an index value of100.0, there is no need to officially use a certain notional amount.Every index value can be converted in any nominal amount bymultiplication. For the calculation of the indices reflecting SpreadTrades and Butterfly Trades however, certain adjustment to the notionalamounts need to be undertaken. Spread trades: The notional amount of thelong leg (which is bought into the index) is set to 25 million USD. Thenotional amount of the short leg (which is sold into the index) isadjusted so that the basis point value of the short leg, at the start ofthe index, or at rebalancing time respectively, (see Rebalancing theIndices below) shall be the same as the basis point value of the longleg. The notional amount of the short leg is rounded to the nearest 0.5million USD. Butterfly trades: The notional amount of the body (which isbought into the index) shall be set to 25 million USD. The body shall beconsidered being divided into two parts of 12.5 million USD each. Thenotional amounts of each of the wings (which are sold into the index) isadjusted so that its basis point value, at the start of the index, or atrebalancing time respectively (see Rebalancing the Indices below), shallbe the same as the basis point value of the half body. The notionalamount of the adjusted legs is rounded to the nearest 0.5 million USD.

Index Data to Publish: The index values start with 100.0 so that achange by 1 would result in an index value of 101.0 or 99.0respectively. The index figures can be considered synthetic.

Ground Rule 2

2.1 Price Sources

2.1.1 Input Data Sources

All calculations are performed using quoted IRS Semi Bond Swap rates,plus standard USD LIBOR rates (Telerate page: 3750) which are used asthe source for interpolations (LIBOR for 1, 2, 3, 6 months and 1 year).The source for IRS Semi Bond Swap rates is the rates displayed onReuters, where there are quotes available for both offer and bid, for2-15 years in steps of 1 year, then for 20, 25 and 30 years. Initiallythe mid swap rates for all these lifetimes are calculated, and then theinterpolations of mid swap rates for the lifetimes of 16-19, 21-24 and26-29 years, using the 15, 20, 25 and 30 year rates respectively arecalculated. These rates are the source for the valuations for allsynthetic swaps, and thus for the calculation of all indices.

On days where there is a business day in NY but not in UK, the LIBORrates of the previous UK business day are used unchanged.

Ground Rule 3

3.1 Rebalancing the Indices

3.1.1 All Index Series US Dollar Indices are rebalanced every month onthe second Wednesday of the month. To avoid cashflows paid out from thesynthetic swap positions, all IRS trades are sold and newly boughtsynthetically once every month. This rebalancing also avoids theshortening of lifetimes of all positions which at beginning are fullyears, so that they can not become less than the respective years (e.g.1+11 months). To avoid deferrals resulting from holidays or weekends,the monthly rebalancing is always done on the second Wednesday of everymonth. The rebalancing procedures, which include the recalculation ofnotional amounts for Spread and Butterfly Trades Indices, shall takeplace on this day at 10.00 NY=16:00 CET=15:00 UK.

3.2 Settings at origin and Resets at rebalance

3.2.1 Interest Rate Swaps semi bond trades

Periods:

2-year, 3-year, 5-year, 10-year, 11-year, 12-year, 30-year, 40-year. Theindex reflects to buy the swap.

Settings at origin:

1. Trade date: Index origin date.

2. Notional principal amount: 1 Million US Dollars.

3. Value date: 2 good business days (spot).

4. Maturity date: The duration of the Interest Rate Swap.

5. Treasury hedge: Current on-the-run.

6. Treasury hedge amount: Determined at Rebalance.

7. Fixed rate: At mid market current treasury yield, plus at mid marketinterest rate swap.

spread to current treasury yield, semi bond.

8. Interest rate swap Spread to current treasury yield: At mid market.

9. Treasury price: At mid market.

10. Treasury yield: At mid market.

11. Fixed rate interest rate calculation: 30/360 adjusted bond basis.

12. Fixed rate payable: Semi annual.

13. Fixed rate payments dates: Semi annual.

14. Floating rate: 3 month LIBOR.

15. First floating rate: LIBOR.

16. First floating rate set for period ending: 3 month LIBOR.

17. Floating rate interest rate calculation: Actual/360.

18. Floating rate reset: Quarterly.

19. Floating rate payable: Quarterly.

20. Floating rate payment dates: Quarterly.

21. Floating rate held and compounded: No.

22. Payment exchange: Net payment.

23. Mutual put: No.

Resets at rebalance:

24. Trade date: The day of the rebalance date.

25. Value date: 2 good business days (spot).

26. Maturity date: The duration of the IRS.

27. Interest Rate Swap spread to current treasury yield: At mid market.

28. Treasury hedge: current on the run.

29. Treasury hedge amount: Determined at Rebalance.

30. Treasury yield: At mid market.

31. Treasury price: At mid market.

32. Fixed rate: At mid market current treasury yield, plus at mid marketinterest rate swap.spread to current treasury yield semi bond.

33. Fixed rate payments dates: Semi annual.

34. Floating rate: 3 month LIBOR.

35. First floating rate set for period ending: 3 month LIBOR.

36. Fixed rate payments dates: Semi annual.

Terms and conditions:

37. Non business day: ISDA documentation.

38. Ref source for interest rate swap spread to current treasury yield:Reuters.

39. Ref source for treasury yield: FTSE.

40. Ref source for floating rate: Telerate page 3750.

41. Conditions: ISDA documentation.

Periods:

4-year, 6-year, 7-year, 8-year, 9-year, 13-year, 14-year, 15-year,16-year, 17-year, 18-year, 19-year,

20-year, 21-year, 22-year, 23-year, 24-year, 25-year, 26-year, 27-year,28-year, and 29-year. The index reflects to buy the swap.

Settings at origin:

1. Trade date: Index origin date.

2. Notional principal amount: 1 Million US Dollars.

3. Value date: 2 good business days (spot).

4. Maturity date: The duration of the Interest Rate Swap.

5. Treasury hedge amount #1.: Determined at Rebalance.

6. Treasury hedge amount #2.: Determined at Rebalance.

7. Fixed rate: At mid market interpolated current treasury yield, plusat mid market interest rate swap spread to current treasury yield semibond.

8. Treasury price #1: At mid market.

9. Treasury price #2: At mid market.

10. Treasury yield #1: At mid market.

11. Treasury yield #2: At mid market.

12. Interpolated treasury yield: At mid market.

13. Interest rate swap spread to current treasury yield: at mid market.

14. Fixed rate interest rate calculation: 30/360 adjusted bond basis.

15. Fixed rate payable: Semi annual.

16. Fixed rate payments dates: Semi annual.

17. Floating rate: 3 month LIBOR.

18. First floating rate: LIBOR.

19. First floating rate set for period ending: 3 month LIBOR.

20. Floating rate interest rate calculation: Actual/360.

21. Floating rate reset: Quarterly.

22. Floating rate payable: Quarterly.

23. Floating rate payment dates: Quarterly.

24. Floating rate held and compounded: No.

25. Payment exchange: Net payment.

26. Mutual put: No.

Resets at rebalance:

27. Trade date: The day of the rebalance date.

28. Value date: 2 good business days (spot).

29. Maturity date: The duration of the IRS. 30. Interest rate swapspread to current treasury yield: At mid market.

31. Treasury hedge amount #1.: Determined at rebalance.

32. Treasury hedge amount #2.: Determined at Rebalance.

33. Treasury hedge #1: Current on the run.

34. Treasury hedge #2: Current on the run.

35. Treasury price #1: At mid market.

36. Treasury price #2: At mid market.

37. Treasury yield #1: At mid market.

38. Treasury yield #2: At mid market.

39. Fixed rate: At mid market current treasury yield, plus at mid marketinterest rate swap spread to current treasury yield, semi bond.

40. Fixed rate payments dates: Semi annual.

41. Floating rate: 3 month LIBOR.

42. First floating rate set for period ending: 3 month LIBOR.

43. Fixed rate payments dates: Semi annual.

Terms and conditions:

44. Non business day: ISDA documentation.

45. Ref source for interest rate swap spread to current treasury yield:Reuters.

46. Ref source for treasury yield: FTSE.

47. Ref source for floating rate: Telerate page 3750.

48. Conditions: ISDA documentation.

49. When there is no current treasury for the IRS period, aninterpolated yield is calculated using the closest current treasurybefore and after the maturity date.

50. When there is no current treasury for the IRS period, the treasuryhedge amount is calculated using a combination of the closest current onthe run treasury before and after the maturity date.

3.2.2 Semi bond spread trades

Periods:

1. 1a) 2-year×3-year. 1b) 2-year×5-year. 1c) 2-year×10-year.

1d) 2-year×30-year.

2. 2a) 3-year×5-year. 2b) 3-year×10-year. 2c) 3-year×30-year.

3. 3a) 5-year×10-year. 3b) 5-year×30-year.

4. 4a) 10-year×30-year.

The IRS spread requires two simultaneous trades buying or selling theshorter period (short leg), whilst trading the reverse selling or buyingthe longer period (long Leg). The index reflects to buy the longerperiod.

Note: not to be confused with a spread to treasury or bid offer spread.

Short leg settings at origin:

1. Trade date: Index origin date.

2. Notional principal amount: Duration weight.

3. Value date: 2 good business days (spot).

4. Maturity date: The duration of the Interest Rate Swap.

5. Treasury hedge: Current on-the-run.

6. Treasury hedge amount: Determined at Rebalance.

7. Fixed rate: At mid market current treasury yield, plus at mid marketinterest rate swap

spread to current treasury yield, semi bond.

8. Interest rate swap spread to current treasury yield: At mid market.

9. Current treasury yield: At mid market.

10. Current treasury price: At mid market.

11. Fixed rate interest rate calculation: 30/360 adjusted bond basis.

12. Fixed rate payable: Semi annual.

13. Fixed rate payments dates: Semi annual.

14. Floating rate: 3 month LIBOR.

15. First floating rate: LIBOR.

16. First floating rate set for period ending: 3 month LIBOR.

17. Floating rate interest rate calculation: Actual/360.

18. Floating rate reset: Quarterly.

19. Floating rate payable: Quarterly.

20. Floating rate payment dates: Quarterly.

21. Floating rate held and compounded: No.

22. Payment exchange: Net payment.

23. Mutual put: No.

Reset at rebalance:

24. Trade date: The day of the rebalance date.

25. Notional principal amount: Duration weight.

26. Value date: 2 good business days (spot).

27. Maturity date: The duration of the IRS.

28. Interest rate swap spread to current treasury yield: At mid market.

29. Treasury hedge: Current on-the-run.

30. Treasury hedge amount: Determined at Rebalance.

31. Treasury price: At mid market

32. Fixed rate: At mid market current treasury yield, plus at mid marketinterest rate swap

spread to current treasury yield, semi bond

33. Fixed rate payments dates: Semi annual.

34. Floating rate: 3 month LIBOR.

35. First floating rate set for period ending: 3 month LIBOR.

36. Floating rate payment dates: Quarterly.

Terms and conditions:

37. Non business day: Modified following ISDA documentation.

38. Ref source for floating rate: Telerate page 3750.

39. Ref source for interest rate swap spread to current treasury yield:Reuters.

40. Ref source for treasury yield: FTSE.

41. Conditions: ISDA documentation.

Long leg settings at origin:

1. Trade date: Index origin date.

2. Notional principal amount: 25 Million US Dollars.

3. Value date: 2 good business days (spot).

4. Maturity date: The duration of the Interest Rate Swap.

5. Treasury hedge: Current on-the-run.

6. Treasury hedge amount: Determined at Rebalance.

7. Fixed rate: At mid market current treasury yield, plus at mid marketinterest rate swap

spread to treasury yield, semi bond.

8. Interest rate swap spread to current treasury yield: At mid market.

9. Treasury yield: At mid market.

10. Treasury price: At mid market.

11. Fixed rate interest rate calculation: 30/360 adjusted bond basis.

12. Fixed rate payable: Semi annual.

13. Fixed rate payments dates: Semi annual.

14. Floating rate: 3 month LIBOR.

15. First floating rate: LIBOR.

16. First floating rate set for period ending: 3 month LIBOR.

17. Floating rate interest rate calculation: Actual/360.

18. Floating rate reset: Quarterly.

19. Floating rate payable: Quarterly.

20. Floating rate payment dates: Quarterly.

21. Floating rate held and compounded: No.

22. Payment exchange: Net payment.

23. Mutual put: No.

Reset at rebalance:

24. Trade date: The day of the rebalance date.

25. Value date: 2 good business days (spot).

26. Maturity date: The duration of the IRS.

27. Interest rate swap spread to current treasury yield: At mid market.

28. Treasury hedge: Current on-the-run.

29. Treasury hedge amount: Determined at Rebalance.

30. Treasury price: At mid market.

31. Fixed rate: At mid market current treasury yield, plus at mid marketinterest rate swap

spread to current treasury yield, semi bond.

32. Fixed rate payments dates: Semi annual.

33. Floating rate: 3 month LIBOR.

34. First floating rate set for period ending: 3 month LIBOR.

35. Floating rate payment dates: Quarterly.

Terms and conditions:

36. Non business day: ISDA documentation.

37. Ref source for interest rate swap spread to current treasury yield:Reuters.

38. Ref source for treasury yield: FTSE.

39. Ref source for floating rate: Telerate page 3750.

40. Conditions: ISDA documentation.

Note: It is standard market practice to apply the notional principleamount to the longer leg with the short leg being duration weighted.

3.2.3 Semi bond butterfly trades

Periods:

1. 1a) 2-year×3-year×5-year. 1b) 2-year×5-year×10-year. 1c)2-year×10-year×30-year.

2. 2a) 3-year×5-year×10-year. 2b) 3-year×10-year×30-year.

3. 3a) 5-year×10-year×30-year.

The IRS butterfly requires three simultaneous trades buying or sellingthe shorter period and longer period, (the wings) whilst trading in theopposite direction, selling or buying the middle period (the body). Theindex reflects to buy the body and sell the wings.

Short wing settings at origin:

1. Trade date: Index origin date.

2. Notional principal amount: Duration weight.

3. Value date: 2 good business days (spot).

4. Maturity date: The duration of the Interest Rate Swap.

5. Treasury hedge: Current on-the-run.

6. Treasury hedge amount: Determined at Rebalance.

7. Fixed rate: At mid market current treasury yield, plus at midinterest rate swap market

spread to current treasury yield, semi bond.

8. Interest rate swap spread to current treasury yield: At mid market.

9. Treasury yield: At mid market.

10. Treasury price: At mid market.

11. Fixed rate interest rate calculation: 30/360 adjusted bond basis.

12. Fixed rate payable: Semi annual.

13. Fixed rate payments dates: Semi annual.

14. Floating rate: 3 month LIBOR.

15. First floating rate: LIBOR.

16. First floating rate set for period ending: 3 month LIBOR.

17. Floating rate interest rate calculation: Actual/360.

18. Floating rate reset: Quarterly.

19. Floating rate payable: Quarterly.

20. Floating rate payment dates: Quarterly.

21. Floating rate held and compounded: No.

22. Payment exchange: Net payment.

23. Mutual put: No.

Reset at rebalance:

24. Trade date: The day of the rebalance date.

25. Notional principal amount: Duration weight.

26. Value date: 2 good business days (spot).

27. Maturity date: The duration of the IRS.

28. Spread to treasury yield: At market.

29. Treasury hedge: Current on-the-run.

30. Treasury hedge amount: Determined at Rebalance.

31. Treasury price: At mid market.

32. Fixed rate: At mid market current treasury yield, plus at mid marketinterest rate swap spread to current treasury yield, semi bond.

33. Fixed rate payments dates: Semi annual.

34. Floating rate: 3 month LIBOR.

35. First floating rate set for period ending: 3 month LIBOR.

36. Floating rate payment dates: Quarterly.

Terms and conditions:

37. Non business day: Modified following ISDA documentation.

38. Ref source for floating rate: Telerate page 3750.

39. Ref source for interest rate swap spread to current treasury yield:Reuters.

40. Ref source for treasury yield: FTSE.

41. Conditions: ISDA documentation.

Body settings at origin:

1. Trade date: Index origin date.

2. Notional principal amount: 25 Million US Dollars.

3. Value date: 2 good business days (spot).

4. Maturity date: The duration of the Interest Rate Swap.

5. Treasury hedge: Current on-the-run.

6. Treasury hedge amount: Determined at Rebalance.

7. Fixed rate: At mid market current treasury yield, plus at mid marketinterest rate swap spread to current treasury yield, semi bond.

8. Interest rate swap spread to current treasury yield: At mid market.

9. Treasury yield: At mid market.

10. Treasury price: At mid market.

11. Fixed rate interest rate calculation: 30/360 adjusted bond basis.

12. Fixed rate payable: Semi annual.

13. Fixed rate payments dates: Semi annual.

14. Floating rate: 3 month LIBOR.

15. First floating rate: LIBOR.

16. First floating rate set for period ending: 3 month LIBOR.

17. Floating rate interest rate calculation: Actual/360.

18. Floating rate reset: Quarterly.

19. Floating rate payable: Quarterly.

20. Floating rate payment dates: Quarterly.

21. Floating rate held and compounded: No.

22. Payment exchange: Net payment.

23. Mutual put: No.

Reset at rebalance:

24. Trade date: The day of the rebalance date.

25. Value date: 2 good business days (spot).

26. Maturity date: The duration of the IRS.

27. Interest rate swap spread to current treasury yield: At mid market.

28. Treasury hedge: Current on-the-run.

29. Treasury hedge amount: Determined at Rebalance.

30. Treasury price: At mid market.

31. Fixed rate: At mid market current treasury yield, plus at mid marketinterest rate swap spread to current treasury yield, semi bond.

32. Fixed rate payments dates: Semi annual.

33. Floating rate: 3 month LIBOR.

34. First floating rate set for period ending: 3 month LIBOR.

35. Floating rate payment dates: Quarterly.

Terms and conditions:

36. Non business day: ISDA documentation.

37. Ref source for interest rate swap spread to current treasury

yield: Reuters.

38. Ref source for treasury yield: FTSE.

39. Ref source for floating rate: Telerate page 3750.

40. Conditions: ISDA documentation.

Long wing settings at origin:

1. Trade date: Index origin date.

2. Notional principal amount: Duration weight.

3. Value date: 2 good business days (spot).

4. Maturity date: The duration of the Interest Rate Swap.

5. Treasury hedge: Current on-the-run.

6. Treasury hedge amount: Determined at Rebalance.

7. Fixed rate: At mid market current treasury yield, plus at mid marketinterest rate swap spread to current treasury yield, semi bond.

8. Interest rate swap spread to current treasury yield: At mid market.

9. Treasury yield: At mid market.

10. Treasury price: At mid market.

11. Fixed rate interest rate calculation: 30/360 adjusted bond basis.

12. Fixed rate payable: Semi annual.

13. Fixed rate payments dates: Semi annual modified following.

14. Floating rate: 3 month LIBOR.

15. First floating rate: LIBOR.

16. First floating rate set for period ending: 3 month LIBOR.

17. Floating rate interest rate calculation: Actual/360.

18. Floating rate reset: Quarterly.

19. Floating rate payable: Quarterly.

20. Floating rate payment dates: Quarterly.

21. Floating rate held and compounded: No.

22. Payment exchange: Net payment.

23. Mutual put: No.

Reset at rebalance:

24. Trade date: The day of the rebalance date.

25. Notional principal amount: Duration weight.

26. Value date: 2 good business days (spot).

27. Maturity date: The duration of the IRS.

28. Interest rate swap spread to current treasury yield: At mid market.

29. Treasury hedge: Current on-the-run.

30. Treasury hedge amount: Determined at Rebalance.

31. Treasury price: At mid market.

32. Fixed rate: At mid market current treasury yield, plus at mid marketinterest rate swap spread to current treasury yield, semi bond.

33. Fixed rate payments dates: Semi annual.

34. Floating rate: 3 month LIBOR.

35. First floating rate set for period ending: 3 month LIBOR.

36. Floating rate payment dates: Quarterly.

Terms and conditions:

37. Non business day: Modified following ISDA documentation.

38. Ref source for floating rate: Telerate page 3750.

39. Ref source for interest rate swap spread to current treasury

yield: Reuters.

40. Ref source for Treasury yield: FTSE.

41. Conditions: ISDA documentation.

Note: It is standard market practice to apply the notional amount to themiddle leg or body, with the wings being duration weighted.

Ground Rule 4 (Amendments and Exceptions)

4.1 In the event that the Bond Index Committee responsible for theoperation and administration of the Index Series US Dollar Indicesconsider that a change of principle or exceptions should be made to anyof the Ground Rules, the issue must be brought to the attention of theChairman or Deputy Chairman of the Bond Index Committee, who willnormally put the matter to the full Bond Index Committee for a decision.

4.2 If, however, the matter is urgent, the Chairman and Deputy Chairman(or their deputies) are collectively empowered to authorise an exceptionon behalf of the Bond Index Committee but must immediately notify, andsubsequently refer the matter to a meeting of the Bond Index Committee.Where an exception is granted to the Ground Rules under Rule 4.1, itshall not be deemed to create a precedent for future decisions of theBond Index Committee.

Thus, a set of indices which accurately reflect the needs of IRS tradershas been created and described herein. The IRS traders who wish tocapture the medium term swap yield curve, this can be done as steepenersor flatteners, may use this set of indices to their advantage in manyways.

In view of the above, it will be seen that the several advantages of theinvention are achieved and other advantages attained. The invention isnot restricted to the above-described embodiments which can be varied ina number of ways within the scope of the invention. As various changescould be made in the above index, derivatives, financial instruments andmethods without departing from the scope of the invention, it isintended that all matter contained in the above description and shown inthe accompanying drawings shall be interpreted as illustrative and notin a limiting sense.

1-75. (canceled)
 76. A system for determining a value of a derivativefinancial instrument, comprising: a. a software package on a computer;b. a real-time interface that connects the computer to a market datasource that supplies market data to the software, the market datacomprising at least one of a first financial instrument bid price and afirst financial instrument offer price, i. a first financial instrumentyield determined by the software from at least one of the firstfinancial instrument bid price and the first financial instrument offerprice; c. a calculating section of the computer that receives the firstfinancial instrument yield from the software and calculates an indexusing the first financial instrument yield in determining a first streamof synthetic future payments from a first leg of a hypothetical swap, i.the calculating section rebalances the index at a predeterminedfrequency by synthetically selling the hypothetical swap andsynthetically rebuying the hypothetical swap; d. a distributioninterface that makes the index available to a plurality of entitiesinterested in the index and enabling a portion of the entities todetermine the value of their derivative financial instrument as aproduct of a notional value of their derivative financial instrument andthe index.
 77. The system of claim 76 further comprising: a. acommunication network connected to the real-time interface and themarket data source through which the market data is retrieved,participation in a market for the first financial instrument beingwidely open, the first financial instrument yield is variable accordingto the market.
 78. The system of claim 76 wherein a second stream ofsynthetic future payments for a second leg of the hypothetical swap isutilized by the calculating section to determine the index.
 79. Thesystem of claim 78 further wherein the calculating section utilizesmodified first and second streams of synthetic future payments thatcorrect for a future value of the first and second streams of syntheticfuture payments in determining the index.
 80. The system of claim 76wherein the swap has at least two legs, the index is calculated at aminimum every business day and the first stream of synthetic futurepayments is determined utilizing mark to market accounting.
 81. Thesystem of claim 76 wherein the first stream of synthetic future paymentscomprises a plurality of payments, each of which is discounted by a zerocoupon bond yield curve prior to calculation of the index.
 82. Thesystem of claim 76 further comprising: a. a single counterparty to allpurchases and sales of the derivative financial instrument.
 83. A systemfor determining a value of a derivative financial instrument,comprising: a. a computer; b. a financial market software packageoperating on the computer; c. a real-time interface connected to thecomputer and, via a network, to a financial instrument market, thefinancial instrument market providing market data to the financialmarket software, d. a calculating section of the computer whichcalculates an index based on a hypothetical swap having two or morelegs, the market data sufficient to calculate a first plurality ofsynthetic future payments for at least a first leg of the hypotheticalswap, the plurality of synthetic future payments utilized in determiningthe index, i. the calculating section determines a rebalance of theindex at a predetermined frequency, the rebalance comprising the resultof a synthetic sale of the hypothetical swap and the synthetic purchaseof the hypothetical swap; e. a distribution interface connected to thecomputer and the network that makes the index available to a pluralityof users, and f. a notional value assigned to the derivative financialinstrument, whereby the value of the derivative financial instrument isa multiplication product of the notional value and the index.
 84. Thesystem of claim 83 further wherein the first leg of the swap has a firstset of parameters that determine the first plurality of synthetic futurepayments; and a second leg of the swap has a second set of parametersthat determine a second plurality of synthetic future payments, thesecond set of parameters including a variable parameter determined fromthe market data and not contained in the first set of parameters. 85.The system of claim 84 wherein the variable parameter is at least one ofa financial instrument price, financial instrument yield and financialinstrument interest rate.
 86. The system of claim 84 wherein the firstset of parameters includes an interest rate having a fixed rate over aterm of the swap.
 87. The system of claim 84 wherein the derivativefinancial instrument is purchased and sold on an essentially transparentmarket.
 88. The system of claim 87 wherein a single counterparty existsto all purchases and sales of the derivative financial instrument. 89.The system of claim 83 wherein the derivative financial instrument iseither a bought financial instrument or a sold financial instrument andfurther wherein the derivative financial instrument value for a boughtfinancial instrument increases proportionally to the index and thederivative financial instrument value for a sold financial instrumentdecreases proportionally to the index.
 90. The system of claim 83wherein the hypothetical swap is for a term, the term being one of thefirst set of parameters and the second set of parameters.
 91. The systemof claim 90 wherein the parameters include a yield curve, the yieldcurve utilized by the software and computer and operating on the firststream of payments.
 92. The system of claim 91 wherein the software andcomputer discounts the first plurality of synthetic future payments by azero coupon bond yield curve.
 93. A system for determining a value of aderivative financial instrument, comprising: a. a software package on acomputer; b. data collecting means for connecting the computer to amarket data source and collecting real-time market data from the marketdata source, the market data sufficient to determine a first financialinstrument yield; c. first payment stream calculating means fordetermining a first stream of synthetic future payments from a first legof a hypothetical swap utilizing the first financial instrument yield;d. second payment stream calculating means for determining a secondstream of synthetic future payments from a second leg of thehypothetical swap; e. index tracking means for calculating an indexutilizing the output from the first and second payment streamcalculating means; f. correction means for rebalancing the index at apredetermined frequency by synthetically selling the hypothetical swapand synthetically rebuying the hypothetical swap; and g. the value ofthe derivative financial instrument determined by multiplying the indexby a notional value.
 94. The system of claim 93 further comprising: a.means for factoring into the index the mark-to-market values of thefirst and second streams of synthetic future payments.